Explanation Given: The vector valued functions are r 1 ( t ) → = t i ^ + t 2 j ^ and r 2 ( t ) → = t 3 i ^ + t 6 j ^ where t = 1 Formula used: If r ( t ) → = x ( t ) i ^ + y ( t ) j ^ + z ( t ) k ^ is the given vector valued function, then the tangent vector to the given curve is d d t ( r ( t ) → ) t = a = [ d d t ( x ( t ) ) i ^ + d d t ( y ( t ) ) j ^ + d d t ( z ( t ) ) k ^ ] t = a Calculation: The vector valued functions are r 1 ( t ) → = t i ^ + t 2 j ^ and r 2 ( t ) → = t 3 i ^ + t 6 j ^ The tangent to the curve r 1 ( t ) → = t i ^ + t 2 j ^ is d d t ( r 1 ( t ) → ) t = a = [ d d t ( x ( t ) ) i ^ + d d t ( y ( t ) ) j ^ ] t = a ⇒ d d t ( r 1 ( t ) → ) t = 1 = [ d d t ( t ) i ^ + d d t ( t 2 ) j ^ ] t = 1 ⇒ d d t ( r 1 ( t ) → ) t = 1 = [ ( 1 ) i ^ + ( 2 t ) j ^ ] t = 1 ⇒ d d t ( r 1 ( t ) → ) t = 1 = [ i ^ + ( 2 × 1 ) j ^ ] ∴ d d t ( r 1 ( t ) → ) t = 1 = [ i ^ + 2 j ^ ] Thus, the tangent vector to the given curve at t = 1 is d d t ( r 1 ( t ) → ) t = 1 = [ i ^ + 2 j ^ ] ...

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Author: Rogawski

Publisher: MAC HIGHER

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magn…

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.

Question

Chapter 14.2, Problem 15E

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The curve associated with the given vector valued function and tangents of the given curve at given point.

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Chapter 14.2, Problem 14E

Chapter 14.2, Problem 16E

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Chapter 14 Solutions

CALCULUS W/SAPLING ACCESS >IC<

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

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The curve associated with the given vector valued function and tangents of the given curve at given point.

Solution Summary: The author calculates the curve associated with the given vector valued function and the tangents of it at a given point.

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The curve associated with the given vector valued function and tangents of the given curve at given point.

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Chapter 14 Solutions